Since the heat conduction in a furnace wall may be regarded as a stochastic process, any boundary or initial condition may be represented by the sum of instantaneous heat sources coming out at the surface or inside of the wall with corresponding temperatures and phase differences.
Therefore, if the probability function of an instantaneous heat source having unit temperature (θ=1), being in existence at the surface or inside of the wall in question, be calculated, the given condition at any point may easily be worked out by the process of simply multiplying the distribution function by the corresponding temperature and superposing the products taking into account of the phase difference and the variation of the temperature.
This paper concerns mainly with the method of getting the probability distribution function mentioned above for the problems of one dimensional right angle coordinates, and the graphical and numerical methods were compared with those of Schmidt, Tanazawa and Takahashi.
This process was also extended to the method of getting the distribution function of unit temperature at any point, making use of the solution of steady heat source problem, and to this end it was proved that the solution of steady boundary conditions may be used to get the corresponding distribution function of instantaneous heat source having unit temperature irrespective of the form of the expression, functional form, empirical form, or any other forms.